The Döppler effect in the extraction of total neutron cross sections from deuterium data with particular emphasis on asymptotic hadron and deep inelastic electron scattering

Abstract

The effects of nuclear Fermi motion on the extraction of high energy neutron cross sections from deuterium data are discussed in some detail. We consider three examples: (i) resonance scattering, (ii) asymptotic hadron scattering and (iii) deep inelastic electron scattering. In the first example we show in a very simple way how a nucleon resonance is broadened when viewed in the deuteron. Simple qualitative expressions are derived for the depression of the peak and the broadening of the width due to the Döppler shifting of the incident energy. For asymptotic hadron scattering, where total cross sections are generally very slowly varying, we show that there is a subtle effect due to the threshold constraint on the total nucleon cross sections which tends to deplete the total deuteron cross section. The size of this defect depends crucially upon the size of the high momentum components in the deuteron wavefunction. The effect is capable of explaining the apparent energy and process dependence of the mean inverse square radius parameter which occurs in the Glauber screening formula. An estimate of the effect in total photoabsorption cross sections indicates that the proton-neutron difference may be considerably smaller than expected. In the third example, deep inelastic electron scattering, this threshold effect increases near the threshold region. This together with the conventional smearing effect is shown to simulate the shape of the apparent difference between the proton and neutron. The size of the overall effect again depends crucially upon the high momentum components in the deuteron. However, reasonable estimates indicate that there is a real proton-neutron difference, especially in the so-called low ω region; the difference probably vanishes in the large ω region. Several other effects in deep inelastic electron scattering are discussed: We show that a value of ω exists (which we call the cross-over point, ω c ) at which the overall effect vanishes. That is, below ω c the effect reverses sign and the neutron cross section now appears larger than it really is. We also derive an expression for the threshold behavior of the deuteron cross section in terms of the threshold behavior of the nucleon cross sections and the asymptotic form of the deuteron elastic form factor. Finally we derive a series of wavefunction independent sum rules which relate the overall integrated depletion to the integrated deuteron cross section below the quasi-elastic peak. Such sum rules could be extremely useful in “measuring” the effects of the Fermi motion. Most of the discussions in the paper are of a qualitative nature; quantitative details will follow in a future publication. The paper has been written with the experimentalist reader in mind.